Niskayuna Central School District > Academics > Niskayuna High School Program of Studies 2026-27 > NHS Program of Studies: 2026-27 Mathematics

NHS Program of Studies: 2026-27 Mathematics

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Grades 9-12 Mathematics Program: A Comprehensive Pathway

The high school mathematics program is structured to provide students with the foundational concepts and advanced skills necessary for mathematical competency and success in higher education. Our curriculum is designed to deepen students’ understanding of core mathematical principles and enhance their analytical and problem-solving capabilities. In collaboration with Schenectady County Community College (SCCC), we offer College in the High School opportunities, enabling students to earn transferable college credit while still attending high school.

Mathematics courses are grouped based on student ability and interest. The Advanced and Honors level courses are specifically designed for students who demonstrate exceptional mathematical proficiency, a strong interest in the subject, and the necessary rigor, perseverance and complex problem-solving skills.

Our department is dedicated to fostering a deep understanding of number systems, developing quantitative reasoning, exploring the nature of mathematical proof and cultivating critical thinking skills. Furthermore, students will gain an appreciation for the historical and ongoing significant contributions of mathematics to human civilization.

The program integrates technology throughout the curriculum, ensuring all students gain practical experience with various technological tools and understand the intrinsic connection between technology and mathematics. To further support this, we offer three distinct computer science courses.

Graduation Requirements

All students are required to earn a minimum of three credits of high school mathematics for graduation. Additionally, students must satisfy the New York State requirement by passing the Algebra I Regents examination. Students must be enrolled in a mathematics course from grades 9 through 11. A student may not withdraw from a mathematics course without enrolling in an alternate mathematics course until they have successfully completed the minimum graduation requirement of three years/three credits.

Calculators

Graphing calculators are required for the New York State Regents examinations in Algebra I, Geometry, and Algebra II, as well as for Advanced Placement examinations. It is highly recommended that students purchase their own calculators. Students planning to own a graphing calculator are strongly encouraged to purchase the TI-84 model, as this is the standard model used by teachers for in-class demonstrations.

Recommendations for Maintaining an Accelerated/Honors Pathway

Ensure students meet the recommended prerequisite grades for moving to the next course in the sequence (e.g., a minimum of 83% is required in PreCalculus Accelerated to stay on the path to AB Calculus).
Ensure that students do not receive a failing grade in any marking period.

Credit By Examination – Algebra I and Geometry

Purpose

The Credit By Examination (CBE) option is available for students currently enrolled in Grade 8 Math, Accelerated Algebra I, or Regents Algebra I who have demonstrated consistent academic success, proficiency in their current mathematics course, and wish to earn high school credit for either Regents Algebra I or Regents Geometry. Students are limited to completing the CBE process only once, which includes summer Precalculus courses.

Overview

This process allows a student to earn a unit of high school mathematics credit without enrolling in the full academic year of the course. This rigorous pathway requires students to master 40 weeks of material within a condensed 6- to 8-week summer period.

Process and Requirements for Credit by Examination

  • Tutor Requirement: Families must engage a New York State Certified Math Teacher to serve as a tutor for this process.
    • A list of recommended tutors will be provided with the official approval letter.
    • The tutor must deliver instruction for all course materials related to the approved math course over a period of 6 to 8 weeks. All learning must occur exclusively with the approved tutor.
    • Please Note: The Niskayuna Central School District is not responsible for the compensation or negotiation of tutoring rates. If concerns arise regarding securing or compensating a tutor, please contact the Director of Mathematics Ashley Rickert. The district is committed to collaborating with families to ensure financial constraints do not preclude participation in this opportunity.
  • Examination: The student is required to achieve a minimum score of 85% on the appropriate NYS Regents examination, administered in August.
  • Portfolio Completion: The student must complete and submit a portfolio prior to the scheduled Regents examination.
  • Submission Deadline: The portfolio must be submitted no later than two business days prior to the administration of the Regents Examination.

Portfolio Requirements

The following components must be included in the student’s portfolio:

  • All completed assignments and materials must be systematically organized in a three-ring binder.
  • A log documenting the time spent by the student working with the approved tutor on required course content. The tutor is responsible for instructing all course materials for the approved math course over a period of 6 to 8 weeks.
  • A comprehensive outline detailing all assigned work for each chapter.
  • A minimum of five completed assignments for each chapter, demonstrating mastery of the concepts. These assignments must be clearly organized by chapter and labeled with the chapter, page, and problem numbers.
    Assignments must reflect proficiency in the chapter’s concepts across a range of cognitive levels.
  • Chapter tests must be included, administered under formal test conditions. The student must show all work as evidence of the problem-solving methods used. The tutor must correct the tests, with the final grade clearly visible.
  • All student work must be presented in a neat and highly organized manner.

Eligibility Criteria

To be considered, students must meet all three of the following criteria:

  1. Current mathematics course average of 95% or greater based on the first three marking periods (Q1, Q2, Q3).
  2. A teacher recommendation by the current mathematics teacher, who affirms the student demonstrates an inquisitive attitude towards learning mathematics, a sustained interest in further mathematics study, and the ability to progress in mathematics with exemplary study skills.
  3. Completed Credit By Exam Application submitted by May 15.

Final Placement Requirement

To be placed in Geometry or Algebra II post CBE, students must successfully complete all components of the Credit by Examination process. Schedule adjustments at Niskayuna High School will not be finalized until late August. Enrollment in the desired course is subject to enrollment priorities and is not guaranteed. If the Credit by Examination requirements are not successfully met, the student will remain in the next course progression as originally scheduled.

Key Dates

Application Deadline: May 15
Decision Notification to Families: June 15
Portfolio Due & Regents Examination: August
Schedule Adjustments Finalized at Niskayuna High School: Late August

Note: enrollment in the desired course is not guaranteed and is subject to scheduling and enrollment priorities.

How to Apply

Applications will be distributed in April through ParentSquare to families of all eligible grade 8 and grade 9 students. All applications will be carefully reviewed and families will receive a decision by June 15. Please submit your completed application no later than May 15.

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Mathematics Full Year Courses

Mathematics Half Year Courses

Computer Science Courses

Mathematics Full Year Courses

21225 ALGEBRA I

1 year, 1 credit, Grades 9-10
NCAA Approved

This course entails a comprehensive study of elementary algebra, linear and quadratic functions, inequalities and absolute value, coordinate geometry, probability and statistics. Additional emphasis is placed on problem solving and algebraic skills. The final examination will be the Algebra I Regents exam taken in June.

21107 INTEGRATED ALGEBRA A

1 year, 1 credit, Grades 9-10
NCAA Approved

This course is the first year of a year and a half sequence leading to the Algebra I Regents exam. The remaining part of the Integrated Algebra curriculum will be completed in the subsequent course, Integrated Algebra B / Geometry A . The main topics of this course are working with variables, solving equations, operations with integers, formulas, polynomials, factoring, graphing elementary relationships, two variable equations, squares and square roots, and statistics. A local final examination is taken at the completion of this course in June. The Algebra I Regents exam will be taken in the Integrated Algebra B/Geometry A course next year.

22107 INTEGRATED ALGEBRA B/GEOMETRY A

1 year, 1 credit, Grades 10-11
NCAA Approved

This course is the second year of a year and a half sequence leading to the Algebra I Regents exam. The second semester will begin the Geometry curriculum. Topics for the first semester include linear and quadratic equations, systems of equations and inequalities, probability and statistics. The focus for the second semester is place and solid figures including area, perimeter and volume, as well as polygons, angles, circles and trigonometry. The Algebra 1 Regents exam will be taken in January.

Prerequisite: Successful completion of Integrated Algebra A

22345 GEOMETRY ACCELERATED

1 year, 1 credit, Grades 9-10
NCAA Approved

This course focuses on the study of Geometry. Topics will include plane and solid figures, congruence, constructions, transformations, deductive proof, similarity, coordinate geometry, trigonometry related triangle laws, circles, and measurement. Since algebra is integrated throughout the course, a high level of proficiency in elementary algebra is expected. This course is intended for students who demonstrate exceptional mathematics skills. The final examination will be the Geometry Regents Exam, which is taken in June.

Prerequisite: Accelerated Algebra; Minimum Final Average of 83% is recommended

22225 GEOMETRY

1 year, 1 credit, Grades 9-11
NCAA Approved

This course focuses on the study of geometry with an integration of algebraic concepts. Topics will include plane and solid figures, congruence, constructions, transformations, deductive proof, similarity, coordinate geometry, trigonometry related triangle laws, circles, and measurement. Since algebra is integrated throughout the course, a proficient level in algebra is expected. This course is intended for students who have completed the Algebra I Course. The final examination will be the Geometry Regents exam, which is taken in June.

Prerequisite: Algebra I; Minimum Final Average of 80% is recommended

23466 ALGEBRA II HONORS

1 year, 1 credit, Grades 9-10
NCAA Approved

This course follows successful completion of Algebra I Accelerated and Geometry Accelerated. It will enrich topics associated with the exploration of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions. Students will also study relationships involving sequences and series and drawing inferences and conclusions from data. It is designed for accelerated tenth-graders who demonstrate exceptional mathematical skills and will include enrichment beyond the Algebra II curriculum. The final examination is a compilation of the midterm exam given in January and the Algebra II Regents exam given in June. Students wishing to receive an Advanced Regents Diploma must take and pass the Algebra II Regents Exam.

Prerequisite: Algebra Accelerated and Geometry Accelerated; Minimum Final Average of 93% in each course is recommended

23346 ALGEBRA II ACCELERATED

1 year, 1 credit, Grades 10-11
NCAA Approved

This course follows successful completion of Algebra I Accelerated and Geometry Accelerated. Units covered will include the exploration of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions. Students will also study relationships involving sequences and series and drawing inferences and conclusions from data. It is designed for accelerated tenth-graders and will include enrichment beyond the Algebra II curriculum. The final examination is a compilation of the midterm exam given in January and the Algebra II Regents exam given in June. Students wishing to receive an Advanced Regents Diploma must take and pass the Algebra II Regents Exam.

Prerequisite: Algebra Accelerated and Geometry Accelerated; Minimum Final Average of 83% in each course is recommended

23226 ALGEBRA II

1 year, 1 credit, Grades 10-12
NCAA Approved

Students in this course will follow the Algebra II Next Generation learning standards adopted by New York State. This course follows successful completion of Algebra I and Geometry. Units covered will include the exploration of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions. Students will also study relationships involving sequences and series and drawing inferences and conclusions from data. Students will take the NYS Next Generation Algebra II Regents Exam in June. The Regents will be the final exam.

Prerequisite: Algebra 1 and Geometry; Minimum Final Average of 75% in each course is recommended

23108 INTRODUCTION TO COLLEGE MATH

1 year, 1 credit, Grades 10-12
NCAA Approved

This course covers intermediate algebra and trigonometry topics. Course material includes the study of functions (linear, quadratic, square root, cubic/cube root, periodic, and exponential), inverses and compositions of functions, operations on real and complex numbers, statistical data analysis, right triangle trigonometry, and periodic functions. Units of study have a calculator and algebraic approach and have a focus on application questions. The final exam is a compilation of exams given in January and June. There is no Regents exam in this course.

Prerequisite: Successful completion of Integrated Algebra B/Geometry A or Geometry

24065 FINANCIAL LITERACY

1 year, 1 credit, Grades 10-12
NCAA Approved

Financial Literacy is a full-year course designed to empower all students with essential skills for economic independence and success. Unlike traditional electives, this algebra-based, applications-oriented, and technology-dependent course uses mathematical modeling to cover core college-preparatory topics from Algebra 2, Statistics, and Precalculus, grounding abstract concepts in real-world power. Students will master high-impact financial strategies across eight umbrellas, including Investing, Credit, Employment & Income Taxes, and Retirement Planning, equipping them with the quantitative reasoning and practical knowledge necessary to navigate complex financial decisions, reduce future debt burdens, and design their own financially successful future after graduation.

Prerequisite: Successful completion of two high school mathematics credits

24465 PRECALCULUS HONORS

1 year, 1 credit, Grades 10-11
NCAA Approved

Students may elect to enroll in the College in the High School program through SCCC, which offers the opportunity to earn 4 college credits via dual enrollment.

This course provides in-depth coverage of the pre-calculus topics: polynomial, rational, exponential, logarithmic and trigonometric functions, polar coordinates, matrices, sequences and series, conics, parametric equations, two-dimensional analytic geometry, and mathematical induction. Students planning to take the AP Calculus BC course should elect this course. A local final examination is taken at the completion of this course in June.

Prerequisite: Algebra II Honors; Minimum Final Average of 83% is recommended

24345 PRECALCULUS ACCELERATED

1 year, 1 credit, Grades 10-11
NCAA Approved

Students may elect to enroll in the College in the High School program through SCCC, which offers the opportunity to earn 4 college credits via dual enrollment.

This course covers the study of two-dimensional analytic geometry, vectors, polar coordinates, polynomial, rational, exponential, logarithmic and trigonometric functions. In addition, complex numbers, DeMoivre’s Theorem, conic sections, matrices and partial fraction decomposition. Students planning to take the AP Calculus AB course should elect this course. A local final examination is taken at the completion of this course in June.

Prerequisite: Algebra II Accelerated; Minimum Final Average of 83% is recommended

24225 PRECALCULUS

1 year, 1 credit, Grades 11-12
NCAA Approved

Students may elect to enroll in the College in the High School program through SCCC, which offers the opportunity to earn 4 college credits via dual enrollment.

Topics to be studied include algebraic and trigonometric functions, trigonometry and its applications, complex numbers, analytic geometry, parametric equations, and polar coordinates. Students planning to take Calculus or planning to continue in a mathematics or science-related field should elect this course. The final examination is a compilation of local exams given in January and June.

Prerequisite: Algebra II; Minimum Final Average of 73% is recommended

26180 AP STATISTICS

1 year, 1 credit, Grades 11-12
NCAA Approved

Students may elect to enroll in the College in the High School program through SCCC, which offers the opportunity to earn 3 college credits via dual enrollment.

This statistics course follows the Advanced Placement syllabus which introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. This course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics and is heavily dependent on graphing calculators and computer technology. This course will be useful for any student considering study in science, engineering, business, psychology or the social sciences. A final examination is taken at the completion of this course. Students will be prepared to take the AP Statistics Exam which is offered in May.

Recommended preparation: Algebra II; Minimum Final Average of a 93%,
Algebra II (A/H); Minimum Final Average of 83%, or Introduction to Data Science; Minimum Final Average of 83%.

24055 INTRODUCTION TO DATA SCIENCE

1 year, 1 credit, Grades 11-12
NCAA Approved

Introduction to Data Science offers students an invaluable opportunity to explore a highly promising and in-demand career trajectory. This course integrates mathematics, statistics, and computational thinking with practical, real-world applications. Serving as an alternative high school mathematics pathway, it equips students with essential data science skills. Students will develop the ability to understand, query, and represent data, focusing on collection, cleanup, transformation, analysis, and visualization. Utilizing Python libraries, students will gain proficiency in writing algorithms, constructing statistical models, and effectively communicating data stories while delving into topics such as machine learning, statistical modeling, data visualization, and programming.

Prerequisite: Successful completion of Geometry

26120 AP CALCULUS BC

1 year, 1 credit, Grade 12
NCAA Approved

Students may elect to enroll in the College in the High School program through SCCC, which offers the opportunity to earn 8 college credits via dual enrollment.

This course completes the topics of the Advanced Placement BC Calculus syllabus started in Precalculus Honors. It is designed to permit the student to take more advanced courses in college, both in mathematics and in subject areas which require an extensive background in mathematics. There will be a local final examination for this course. The BC Advanced Placement examination is offered in May.

Prerequisite: Precalculus Honors; Minimum Final Average of 83% is recommended

26100 AP CALCULUS AB

1 year, 1 credit, Grade 12
NCAA Approved

Students may elect to enroll in the College in the High School program through SCCC, which offers the opportunity to earn 4 college credits via dual enrollment.

This is a Calculus course that follows the Advanced Placement AB Calculus syllabus. This course is designed to permit the student to take more advanced courses in college, both in mathematics and in subject areas which require an extensive background in mathematics. There will be a local final examination for this course. The AB Advanced Placement examination is offered in May.

Prerequisite: Precalculus Accelerated; Minimum Final Average of 83% is recommended

26020 CALCULUS

1 year, 1 credit, Grade 12
NCAA Approved

Students may elect to enroll in the College in the High School program through SCCC, which offers the opportunity to earn 4 college credits via dual enrollment.

This course covers the study of Calculus topics such as functions, limits and continuity, differentiation and integration. It is designed to permit the student to take more advanced courses in college, both in mathematics and subject areas that require a background in mathematics. The final examination is a compilation of local exams given in January and June. 

Prerequisite: Precalculus; Minimum Final Average of 80% is recommended

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Mathematics Half Year Courses

26445 MULTIVARIABLE CALCULUS (CALCULUS 3)

1 Semester, 1/2 credit, Grade 12
NCAA Approved

Multivariable Calculus requires a significant jump in higher-order thinking by demanding advanced spatial reasoning to visualize and manipulate functions, vectors, and surfaces in three dimensions. Success relies on the conceptual synthesis of all prior math, algebra, trig, and single-variable calculus, to solve problems with multiple variables. Students must employ non-routine problem-solving and critical thinking to strategically choose the correct tool (like coordinate systems or theorems) for modeling and solving complex, multi-step problems that extend the rules of differentiation and integration into 3D space.Topics include graphing 3-D graphing, vectors and applications, derivatives of multivariable functions, multivariable optimization, multiple integrals, vector fields, and the theorems of Green, Gauss and Stokes.

Prerequisite: AP Calculus AB; Minimum Final Average of an 83% is recommended or Successful Completion of the First Semester of AP Calculus BC.

24110 INTRODUCTION TO PRECALCULUS

1 semester, 1/2 credit, Grades 11-12
NCAA Approved

The main purpose for this course is to help prepare students for a college level math course. The curriculum will strengthen student’s skills introduced in their previous course curricula and extend them into the traditional Pre Calculus domain. The mathematical investigations will take a graphing calculator approach with emphasis on mathematical applications. Topics to be investigated will include: Analytic Trigonometry, polynomial functions and their graphs, rational functions and their graphs, exponential functions and logarithmic functions. The final exam is a compilation of two half-course exams. There is no Regents exam for this course.

Prerequisite: Successful completion of Algebra II or Intro to College Math

24050 INTRODUCTION TO STATISTICS

1 semester, 1/2 credit, Grades 11-12
NCAA Approved

This course is designed as an introduction to descriptive and inferential statistics. Topics for discussion during the first quarter will include: data sources and ways of representing data, measures of central tendency and their applications, normal distributions, and linear regression. During the second quarter we will discuss: probability concepts including binomial distributions and conditional probability, expected value, confidence intervals, and hypothesis testing. Handheld and appropriate computer technologies, such as Excel, will be utilized. The final exam is a compilation of two half-course exams. There is no Regents exam for this course.

Prerequisite: Successful completion of Algebra II or Intro to College Math

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COMPUTER SCIENCE COURSES

27100 COMPUTER SCIENCE 1

1 semester, 1/2 credit, Grades 9-12

At Niskayuna we constantly are striving to introduce our students to the field of computer science. The course starts off utilizing HTML and CSS, so students can see the end result using an Internet Browser and design a website. The course then transitions into graphical programming environments known as Karel and Snap!, followed by an introduction to object-oriented programming using Python. These languages are a gentle approach to learning the structure and syntax of JAVA. Students will develop games starting with Snap!. Students utilize their computational thinking to design their website, games and programs. Computational thinking techniques include: problem decomposition, pattern recognition, pattern generalization to define abstractions or models, algorithm design, and data analysis and visualization.

Prerequisite: Successful completion of Algebra or Integrated Algebra A

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27120 COMPUTER SCIENCE 2

1 semester, 1/2 credit, Grades 9-12

A continuation of computer science one with an emphasis on computational thinking with Java and Processing languages utilized as a vehicle for algorithm implementation. The class prepares students for later computer science classes such as APCS A or introductory computer science in college.

Prerequisite: Successful completion of Computer Science 1 or an exemption test given by the instructor.

27140 AP COMPUTER SCIENCE A

1 year, 1 credit, Grades 10-12

Students may elect to enroll in the College in the High School program through SCCC, which offers the opportunity to earn 3 college credits via dual enrollment.

AP Computer Science goes beyond merely learning how to use applications like word processing, spreadsheets, and internet browsers. It uses the Java language and focuses on the principles needed to design and build programs with an object-oriented language. Students explore class construction, arrays, ArrayLists, polymorphism and recursion. It is taught as a college level course. At the course’s end, students have the option to take the AP Computer Science A exam which is offered in May. Additionally, students have the opportunity to receive college credit for one semester of computer science.

Recommended preparation: Successful completion of Computer Science 1 and Computer Science 2 or demonstration of a solid understanding of Java to the instructor.

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